MODULE dynzdf !!============================================================================== !! *** MODULE dynzdf *** !! Ocean dynamics : vertical component of the momentum mixing trend !!============================================================================== !! History : 1.0 ! 2005-11 (G. Madec) Original code !! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase !! 4.0 ! 2017-06 (G. Madec) remove the explicit time-stepping option + avm at t-point !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! dyn_zdf : compute the after velocity through implicit calculation of vertical mixing !!---------------------------------------------------------------------- USE oce ! ocean dynamics and tracers variables USE phycst ! physical constants USE dom_oce ! ocean space and time domain variables USE sbc_oce ! surface boundary condition: ocean USE zdf_oce ! ocean vertical physics variables USE zdfdrg ! vertical physics: top/bottom drag coef. USE dynadv ,ONLY: ln_dynadv_vec ! dynamics: advection form USE dynldf_iso,ONLY: akzu, akzv ! dynamics: vertical component of rotated lateral mixing USE ldfdyn ! lateral diffusion: eddy viscosity coef. and type of operator USE trd_oce ! trends: ocean variables USE trddyn ! trend manager: dynamics ! USE in_out_manager ! I/O manager USE lib_mpp ! MPP library USE prtctl ! Print control USE timing ! Timing IMPLICIT NONE PRIVATE PUBLIC dyn_zdf ! routine called by step.F90 REAL(wp) :: r_vvl ! non-linear free surface indicator: =0 if ln_linssh=T, =1 otherwise !! * Substitutions # include "do_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OCE 4.0 , NEMO Consortium (2018) !! $Id$ !! Software governed by the CeCILL license (see ./LICENSE) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE dyn_zdf( kt, Kbb, Kmm, Krhs, puu, pvv, Kaa ) !!---------------------------------------------------------------------- !! *** ROUTINE dyn_zdf *** !! !! ** Purpose : compute the trend due to the vert. momentum diffusion !! together with the Leap-Frog time stepping using an !! implicit scheme. !! !! ** Method : - Leap-Frog time stepping on all trends but the vertical mixing !! u(after) = u(before) + 2*dt * u(rhs) vector form or linear free surf. !! u(after) = ( e3u_b*u(before) + 2*dt * e3u_n*u(rhs) ) / e3u(after) otherwise !! - update the after velocity with the implicit vertical mixing. !! This requires to solver the following system: !! u(after) = u(after) + 1/e3u(after) dk+1[ mi(avm) / e3uw(after) dk[ua] ] !! with the following surface/top/bottom boundary condition: !! surface: wind stress input (averaged over kt-1/2 & kt+1/2) !! top & bottom : top stress (iceshelf-ocean) & bottom stress (cf zdfdrg.F90) !! !! ** Action : (puu(:,:,:,Kaa),pvv(:,:,:,Kaa)) after velocity !!--------------------------------------------------------------------- INTEGER , INTENT( in ) :: kt ! ocean time-step index INTEGER , INTENT( in ) :: Kbb, Kmm, Krhs, Kaa ! ocean time level indices REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation ! INTEGER :: ji, jj, jk ! dummy loop indices INTEGER :: iku, ikv ! local integers REAL(wp) :: zzwi, ze3ua, zdt ! local scalars REAL(wp) :: zzws, ze3va ! - - REAL(wp) :: z1_e3ua, z1_e3va ! - - REAL(wp) :: zWu , zWv ! - - REAL(wp) :: zWui, zWvi ! - - REAL(wp) :: zWus, zWvs ! - - REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zwd, zws ! 3D workspace REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdu, ztrdv ! - - !!--------------------------------------------------------------------- ! IF( ln_timing ) CALL timing_start('dyn_zdf') ! IF( kt == nit000 ) THEN !* initialization IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'dyn_zdf_imp : vertical momentum diffusion implicit operator' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ ' ! If( ln_linssh ) THEN ; r_vvl = 0._wp ! non-linear free surface indicator ELSE ; r_vvl = 1._wp ENDIF ENDIF ! !* set time step IF( neuler == 0 .AND. kt == nit000 ) THEN ; r2dt = rdt ! = rdt (restart with Euler time stepping) ELSEIF( kt <= nit000 + 1 ) THEN ; r2dt = 2. * rdt ! = 2 rdt (leapfrog) ENDIF ! ! !* explicit top/bottom drag case IF( .NOT.ln_drgimp ) CALL zdf_drg_exp( kt, Kmm, puu(:,:,:,Kbb), pvv(:,:,:,Kbb), puu(:,:,:,Krhs), pvv(:,:,:,Krhs) ) ! add top/bottom friction trend to (puu(Kaa),pvv(Kaa)) ! ! IF( l_trddyn ) THEN !* temporary save of ta and sa trends ALLOCATE( ztrdu(jpi,jpj,jpk), ztrdv(jpi,jpj,jpk) ) ztrdu(:,:,:) = puu(:,:,:,Krhs) ztrdv(:,:,:) = pvv(:,:,:,Krhs) ENDIF ! ! !== RHS: Leap-Frog time stepping on all trends but the vertical mixing ==! (put in puu(:,:,:,Kaa),pvv(:,:,:,Kaa)) ! ! ! time stepping except vertical diffusion IF( ln_dynadv_vec .OR. ln_linssh ) THEN ! applied on velocity DO jk = 1, jpkm1 puu(:,:,jk,Kaa) = ( puu(:,:,jk,Kbb) + r2dt * puu(:,:,jk,Krhs) ) * umask(:,:,jk) pvv(:,:,jk,Kaa) = ( pvv(:,:,jk,Kbb) + r2dt * pvv(:,:,jk,Krhs) ) * vmask(:,:,jk) END DO ELSE ! applied on thickness weighted velocity DO jk = 1, jpkm1 puu(:,:,jk,Kaa) = ( e3u(:,:,jk,Kbb) * puu(:,:,jk,Kbb) & & + r2dt * e3u(:,:,jk,Kmm) * puu(:,:,jk,Krhs) ) / e3u(:,:,jk,Kaa) * umask(:,:,jk) pvv(:,:,jk,Kaa) = ( e3v(:,:,jk,Kbb) * pvv(:,:,jk,Kbb) & & + r2dt * e3v(:,:,jk,Kmm) * pvv(:,:,jk,Krhs) ) / e3v(:,:,jk,Kaa) * vmask(:,:,jk) END DO ENDIF ! ! add top/bottom friction ! With split-explicit free surface, barotropic stress is treated explicitly Update velocities at the bottom. ! J. Chanut: The bottom stress is computed considering after barotropic velocities, which does ! not lead to the effective stress seen over the whole barotropic loop. ! G. Madec : in linear free surface, e3u(:,:,:,Kaa) = e3u(:,:,:,Kmm) = e3u_0, so systematic use of e3u(:,:,:,Kaa) IF( ln_drgimp .AND. ln_dynspg_ts ) THEN DO jk = 1, jpkm1 ! remove barotropic velocities puu(:,:,jk,Kaa) = ( puu(:,:,jk,Kaa) - uu_b(:,:,Kaa) ) * umask(:,:,jk) pvv(:,:,jk,Kaa) = ( pvv(:,:,jk,Kaa) - vv_b(:,:,Kaa) ) * vmask(:,:,jk) END DO DO_2D_00_00 iku = mbku(ji,jj) ! ocean bottom level at u- and v-points ikv = mbkv(ji,jj) ! (deepest ocean u- and v-points) ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) + r_vvl * e3u(ji,jj,iku,Kaa) ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) + r_vvl * e3v(ji,jj,ikv,Kaa) puu(ji,jj,iku,Kaa) = puu(ji,jj,iku,Kaa) + r2dt * 0.5*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) * uu_b(ji,jj,Kaa) / ze3ua pvv(ji,jj,ikv,Kaa) = pvv(ji,jj,ikv,Kaa) + r2dt * 0.5*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) * vv_b(ji,jj,Kaa) / ze3va END_2D IF( ln_isfcav ) THEN ! Ocean cavities (ISF) DO_2D_00_00 iku = miku(ji,jj) ! top ocean level at u- and v-points ikv = mikv(ji,jj) ! (first wet ocean u- and v-points) ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) + r_vvl * e3u(ji,jj,iku,Kaa) ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) + r_vvl * e3v(ji,jj,ikv,Kaa) puu(ji,jj,iku,Kaa) = puu(ji,jj,iku,Kaa) + r2dt * 0.5*( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) * uu_b(ji,jj,Kaa) / ze3ua pvv(ji,jj,ikv,Kaa) = pvv(ji,jj,ikv,Kaa) + r2dt * 0.5*( rCdU_top(ji,jj+1)+rCdU_top(ji,jj) ) * vv_b(ji,jj,Kaa) / ze3va END_2D END IF ENDIF ! ! !== Vertical diffusion on u ==! ! ! !* Matrix construction zdt = r2dt * 0.5 IF( ln_zad_Aimp ) THEN !! SELECT CASE( nldf_dyn ) CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) DO_3D_00_00( 1, jpkm1 ) ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) + r_vvl * e3u(ji,jj,jk,Kaa) ! after scale factor at U-point zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) + akzu(ji,jj,jk ) ) & & / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk ) zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) + akzu(ji,jj,jk+1) ) & & / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1) zWui = ( wi(ji,jj,jk ) + wi(ji+1,jj,jk ) ) / ze3ua zWus = ( wi(ji,jj,jk+1) + wi(ji+1,jj,jk+1) ) / ze3ua zwi(ji,jj,jk) = zzwi + zdt * MIN( zWui, 0._wp ) zws(ji,jj,jk) = zzws - zdt * MAX( zWus, 0._wp ) zwd(ji,jj,jk) = 1._wp - zzwi - zzws + zdt * ( MAX( zWui, 0._wp ) - MIN( zWus, 0._wp ) ) END_3D CASE DEFAULT ! iso-level lateral mixing DO_3D_00_00( 1, jpkm1 ) ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) + r_vvl * e3u(ji,jj,jk,Kaa) ! after scale factor at U-point zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) ) / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk ) zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) ) / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1) zWui = ( wi(ji,jj,jk ) + wi(ji+1,jj,jk ) ) / ze3ua zWus = ( wi(ji,jj,jk+1) + wi(ji+1,jj,jk+1) ) / ze3ua zwi(ji,jj,jk) = zzwi + zdt * MIN( zWui, 0._wp ) zws(ji,jj,jk) = zzws - zdt * MAX( zWus, 0._wp ) zwd(ji,jj,jk) = 1._wp - zzwi - zzws + zdt * ( MAX( zWui, 0._wp ) - MIN( zWus, 0._wp ) ) END_3D END SELECT DO_2D_00_00 zwi(ji,jj,1) = 0._wp ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,1,Kmm) + r_vvl * e3u(ji,jj,1,Kaa) zzws = - zdt * ( avm(ji+1,jj,2) + avm(ji ,jj,2) ) / ( ze3ua * e3uw(ji,jj,2,Kmm) ) * wumask(ji,jj,2) zWus = ( wi(ji ,jj,2) + wi(ji+1,jj,2) ) / ze3ua zws(ji,jj,1 ) = zzws - zdt * MAX( zWus, 0._wp ) zwd(ji,jj,1 ) = 1._wp - zzws - zdt * ( MIN( zWus, 0._wp ) ) END_2D ELSE SELECT CASE( nldf_dyn ) CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) DO_3D_00_00( 1, jpkm1 ) ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) + r_vvl * e3u(ji,jj,jk,Kaa) ! after scale factor at U-point zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) + akzu(ji,jj,jk ) ) & & / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk ) zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) + akzu(ji,jj,jk+1) ) & & / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1) zwi(ji,jj,jk) = zzwi zws(ji,jj,jk) = zzws zwd(ji,jj,jk) = 1._wp - zzwi - zzws END_3D CASE DEFAULT ! iso-level lateral mixing DO_3D_00_00( 1, jpkm1 ) ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) + r_vvl * e3u(ji,jj,jk,Kaa) ! after scale factor at U-point zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) ) / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk ) zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) ) / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1) zwi(ji,jj,jk) = zzwi zws(ji,jj,jk) = zzws zwd(ji,jj,jk) = 1._wp - zzwi - zzws END_3D END SELECT DO_2D_00_00 zwi(ji,jj,1) = 0._wp zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) END_2D ENDIF ! ! ! !== Apply semi-implicit bottom friction ==! ! ! Only needed for semi-implicit bottom friction setup. The explicit ! bottom friction has been included in "u(v)a" which act as the R.H.S ! column vector of the tri-diagonal matrix equation ! IF ( ln_drgimp ) THEN ! implicit bottom friction DO_2D_00_00 iku = mbku(ji,jj) ! ocean bottom level at u- and v-points ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) + r_vvl * e3u(ji,jj,iku,Kaa) ! after scale factor at T-point zwd(ji,jj,iku) = zwd(ji,jj,iku) - r2dt * 0.5*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) / ze3ua END_2D IF ( ln_isfcav ) THEN ! top friction (always implicit) DO_2D_00_00 !!gm top Cd is masked (=0 outside cavities) no need of test on mik>=2 ==>> it has been suppressed iku = miku(ji,jj) ! ocean top level at u- and v-points ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) + r_vvl * e3u(ji,jj,iku,Kaa) ! after scale factor at T-point zwd(ji,jj,iku) = zwd(ji,jj,iku) - r2dt * 0.5*( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) / ze3ua END_2D END IF ENDIF ! ! Matrix inversion starting from the first level !----------------------------------------------------------------------- ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) ! ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) ! ( ... )( ... ) ( ... ) ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) ! ! m is decomposed in the product of an upper and a lower triangular matrix ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi ! The solution (the after velocity) is in puu(:,:,:,Kaa) !----------------------------------------------------------------------- ! DO_3D_00_00( 2, jpkm1 ) zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1) END_3D ! DO_2D_00_00 ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,1,Kmm) + r_vvl * e3u(ji,jj,1,Kaa) puu(ji,jj,1,Kaa) = puu(ji,jj,1,Kaa) + r2dt * 0.5_wp * ( utau_b(ji,jj) + utau(ji,jj) ) & & / ( ze3ua * rau0 ) * umask(ji,jj,1) END_2D DO_3D_00_00( 2, jpkm1 ) puu(ji,jj,jk,Kaa) = puu(ji,jj,jk,Kaa) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * puu(ji,jj,jk-1,Kaa) END_3D ! DO_2D_00_00 puu(ji,jj,jpkm1,Kaa) = puu(ji,jj,jpkm1,Kaa) / zwd(ji,jj,jpkm1) END_2D DO_3DS_00_00( jpk-2, 1, -1 ) puu(ji,jj,jk,Kaa) = ( puu(ji,jj,jk,Kaa) - zws(ji,jj,jk) * puu(ji,jj,jk+1,Kaa) ) / zwd(ji,jj,jk) END_3D ! ! !== Vertical diffusion on v ==! ! ! !* Matrix construction zdt = r2dt * 0.5 IF( ln_zad_Aimp ) THEN !! SELECT CASE( nldf_dyn ) CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzv) DO_3D_00_00( 1, jpkm1 ) ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) + akzv(ji,jj,jk ) ) & & / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk ) zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) + akzv(ji,jj,jk+1) ) & & / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1) zWvi = ( wi(ji,jj,jk ) + wi(ji,jj+1,jk ) ) / ze3va zWvs = ( wi(ji,jj,jk+1) + wi(ji,jj+1,jk+1) ) / ze3va zwi(ji,jj,jk) = zzwi + zdt * MIN( zWvi, 0._wp ) zws(ji,jj,jk) = zzws - zdt * MAX( zWvs, 0._wp ) zwd(ji,jj,jk) = 1._wp - zzwi - zzws - zdt * ( - MAX( zWvi, 0._wp ) + MIN( zWvs, 0._wp ) ) END_3D CASE DEFAULT ! iso-level lateral mixing DO_3D_00_00( 1, jpkm1 ) ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) ) / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk ) zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) ) / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1) zWvi = ( wi(ji,jj,jk ) + wi(ji,jj+1,jk ) ) / ze3va zWvs = ( wi(ji,jj,jk+1) + wi(ji,jj+1,jk+1) ) / ze3va zwi(ji,jj,jk) = zzwi + zdt * MIN( zWvi, 0._wp ) zws(ji,jj,jk) = zzws - zdt * MAX( zWvs, 0._wp ) zwd(ji,jj,jk) = 1._wp - zzwi - zzws - zdt * ( - MAX( zWvi, 0._wp ) + MIN( zWvs, 0._wp ) ) END_3D END SELECT DO_2D_00_00 zwi(ji,jj,1) = 0._wp ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,1,Kmm) + r_vvl * e3v(ji,jj,1,Kaa) zzws = - zdt * ( avm(ji,jj+1,2) + avm(ji,jj,2) ) / ( ze3va * e3vw(ji,jj,2,Kmm) ) * wvmask(ji,jj,2) zWvs = ( wi(ji,jj ,2) + wi(ji,jj+1,2) ) / ze3va zws(ji,jj,1 ) = zzws - zdt * MAX( zWvs, 0._wp ) zwd(ji,jj,1 ) = 1._wp - zzws - zdt * ( MIN( zWvs, 0._wp ) ) END_2D ELSE SELECT CASE( nldf_dyn ) CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) DO_3D_00_00( 1, jpkm1 ) ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) + akzv(ji,jj,jk ) ) & & / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk ) zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) + akzv(ji,jj,jk+1) ) & & / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1) zwi(ji,jj,jk) = zzwi zws(ji,jj,jk) = zzws zwd(ji,jj,jk) = 1._wp - zzwi - zzws END_3D CASE DEFAULT ! iso-level lateral mixing DO_3D_00_00( 1, jpkm1 ) ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) ) / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk ) zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) ) / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1) zwi(ji,jj,jk) = zzwi zws(ji,jj,jk) = zzws zwd(ji,jj,jk) = 1._wp - zzwi - zzws END_3D END SELECT DO_2D_00_00 zwi(ji,jj,1) = 0._wp zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) END_2D ENDIF ! ! !== Apply semi-implicit top/bottom friction ==! ! ! Only needed for semi-implicit bottom friction setup. The explicit ! bottom friction has been included in "u(v)a" which act as the R.H.S ! column vector of the tri-diagonal matrix equation ! IF( ln_drgimp ) THEN DO_2D_00_00 ikv = mbkv(ji,jj) ! (deepest ocean u- and v-points) ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) + r_vvl * e3v(ji,jj,ikv,Kaa) ! after scale factor at T-point zwd(ji,jj,ikv) = zwd(ji,jj,ikv) - r2dt * 0.5*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) / ze3va END_2D IF ( ln_isfcav ) THEN DO_2D_00_00 ikv = mikv(ji,jj) ! (first wet ocean u- and v-points) ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) + r_vvl * e3v(ji,jj,ikv,Kaa) ! after scale factor at T-point zwd(ji,jj,ikv) = zwd(ji,jj,ikv) - r2dt * 0.5*( rCdU_top(ji,jj+1)+rCdU_top(ji,jj) ) / ze3va END_2D ENDIF ENDIF ! Matrix inversion !----------------------------------------------------------------------- ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) ! ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) ! ( ... )( ... ) ( ... ) ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) ! ! m is decomposed in the product of an upper and lower triangular matrix ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi ! The solution (after velocity) is in 2d array va !----------------------------------------------------------------------- ! DO_3D_00_00( 2, jpkm1 ) zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1) END_3D ! DO_2D_00_00 ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,1,Kmm) + r_vvl * e3v(ji,jj,1,Kaa) pvv(ji,jj,1,Kaa) = pvv(ji,jj,1,Kaa) + r2dt * 0.5_wp * ( vtau_b(ji,jj) + vtau(ji,jj) ) & & / ( ze3va * rau0 ) * vmask(ji,jj,1) END_2D DO_3D_00_00( 2, jpkm1 ) pvv(ji,jj,jk,Kaa) = pvv(ji,jj,jk,Kaa) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * pvv(ji,jj,jk-1,Kaa) END_3D ! DO_2D_00_00 pvv(ji,jj,jpkm1,Kaa) = pvv(ji,jj,jpkm1,Kaa) / zwd(ji,jj,jpkm1) END_2D DO_3DS_00_00( jpk-2, 1, -1 ) pvv(ji,jj,jk,Kaa) = ( pvv(ji,jj,jk,Kaa) - zws(ji,jj,jk) * pvv(ji,jj,jk+1,Kaa) ) / zwd(ji,jj,jk) END_3D ! IF( l_trddyn ) THEN ! save the vertical diffusive trends for further diagnostics ztrdu(:,:,:) = ( puu(:,:,:,Kaa) - puu(:,:,:,Kbb) ) / r2dt - ztrdu(:,:,:) ztrdv(:,:,:) = ( pvv(:,:,:,Kaa) - pvv(:,:,:,Kbb) ) / r2dt - ztrdv(:,:,:) CALL trd_dyn( ztrdu, ztrdv, jpdyn_zdf, kt, Kmm ) DEALLOCATE( ztrdu, ztrdv ) ENDIF ! ! print mean trends (used for debugging) IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=puu(:,:,:,Kaa), clinfo1=' zdf - Ua: ', mask1=umask, & & tab3d_2=pvv(:,:,:,Kaa), clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) ! IF( ln_timing ) CALL timing_stop('dyn_zdf') ! END SUBROUTINE dyn_zdf !!============================================================================== END MODULE dynzdf